(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A point mass m moving along the z axis experiences a time dependent force and a fricitional force. Solve the equation of motion

m[itex]\ddot{z}[/itex] = -m[itex]\gamma[/itex][itex]\dot{z}[/itex] + F(t)

to find v(t) = [itex]\dot{z}[/itex](t) for the initial velocity [itex]\dot{z}[/itex](0) = v_0

Hint: what is the time derivative of [itex]e^{\gamma t}[/itex]v(t)

3. The attempt at a solution

So I made use of the hint and got [itex]e^{\gamma t}[/itex] ([itex]\ddot{z}[/itex](t) + [itex]\gamma[/itex][itex]\dot{z}[/itex](t) )

Manipulating the equation of motion, I got [itex]e^{\gamma t}[/itex] ([itex]\ddot{z}[/itex](t) + [itex]\gamma[/itex][itex]\dot{z}[/itex](t) ) = [itex]e^{\gamma t}[/itex] 1/m F(t)

Subbing in the hint and integrating: [itex]\dot{z}[/itex](t) = [itex]e^{-\gamma t}[/itex]/m [itex]\int[/itex] [itex]e^{\gamma t}[/itex] F(t) dt

Just wondering if this is correct? and how do I make use of the initial condition v_0?

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# Homework Help: Classical mechanics equation of motion

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